Physics of Biological Oscillators: New Insights into Non-Equilibrium and Non-Autonomous Systems [Paperback]

This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment.  Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described.

Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas. 

Chapter 1. Introduction.- Part 1. Theory.- Chapter 2. Phase and amplitude description of complex oscillatory patterns in reaction diffusion systems.- Chapter 3. Reduced phase models of oscillatory neural networks.- Chapter 4. Nonautonomous attractors.- Chapter 5. Normal hyperbolicity for non-autonomous oscillators and oscillator networks.- Chapter 6. Synchronisation and non-autonomicity.- Chapter 7. Non-asymptotic-time dynamics.- Chapter 8. Synchronization of coupled oscillators  phase transitions and entropy production.- Part 2. Model-Driven and Data-Driven approaches.- Chapter 9. On localised modes in bio-inspired hierarchically organised oscillatory chains.- Chapter 10. Useful transformations from non-autonomous to autonomous systems.- Chapter 11. Coupling functions in neuroscience.- Chapter 12. Phase reconstruction with iterated Hilbert transforms.- Part 3. Biological Oscillators.- Chapter 13. Oscillations in yeast glycolysis Lars Folke Olsen and Anita Lunding.- Chapter 14. Oscillations, rhyl#%